A variety of offshore terminals have been proposed for mooring a vessel, especially to enable transferance of fluids between the vessel and a pipe at the sea floor or another vessel. One of the simplest and potentially lowest cost systems includes a transfer structure coupled to the vessel, a single anchor line extending down from the transfer structure, and a group of chains for holding the lower end of the anchor line and allowing its limited movement as the vessel drifts. U.S. Pat. No. 3,979,785 describes a system of this type. However, none of such simple systems have been successfully marketed. One problem has been that while the use of loose chains to hold the bottom of an anchor line minimizes the amount of chain, especially in deep waters, the reduced amount of chain results in only a low restoring force, urging the drifting vessel back towards the quiescent position of the system. Another problem is that the long vertical anchor line can be twisted as a ship drifts around the anchor line. Yet another problem is that it has been difficult to set up the system and test it. It has been even more difficult to re-establish connection to a vessel after the vessel has sailed away and then returned. A practical single anchor line mooring system would have considerable value.